Possible divergences in Tsallis' thermostatistics

Abstract

Lutsko and Boon have shown via elegant theoretical reasoning (EPL, 95 (2011) 20006), that Tsallis’ thermostatistics is affected by divergence problems. We explicitly verify such fact in trying to compute the nonextensive q-partition function for the harmonic oscillator in more than two dimensions. One can see that it indeed diverges. The appeal to the so-called q-Laplace transform, where the q-exponential function plays the role of the ordinary exponential, is seen to overcome the serious problem envisaged by Lutsko and Boon.